Question

Classify the following sequence as arithmetic, geometric, neither or both: 2, 6, 18, ...

Arithmetic

Geometric

Neither

Both

Answer 1

Geometric

Explanation:

Does multiplying the same number with each term give the next term?

If so, then it is Geometric Sequence.

Does adding the same number with each term give the next term?

If so, then it is Arithmetic Sequence.

We see that multiplying by 3 gives us each successive term. 2 times 3 is 6 and 6 times 3 is 18. So it is geometric sequence.

It is NOT arithmetic sequence since we add 4 to 2 to get next number 6, but we have 12 to get next number, which is 18. So not an arithmetic sequence.

Answer is "Geometric"